Signal, Image and Video Processing

, Volume 6, Issue 3, pp 343–350 | Cite as

Introducing the fractional-order Darwinian PSO

  • Micael S. CouceiroEmail author
  • Rui P. Rocha
  • N. M. Fonseca Ferreira
  • J. A. Tenreiro Machado
Original Paper


One of the most well-known bio-inspired algorithms used in optimization problems is the particle swarm optimization (PSO), which basically consists on a machine-learning technique loosely inspired by birds flocking in search of food. More specifically, it consists of a number of particles that collectively move on the search space in search of the global optimum. The Darwinian particle swarm optimization (DPSO) is an evolutionary algorithm that extends the PSO using natural selection, or survival of the fittest, to enhance the ability to escape from local optima. This paper firstly presents a survey on PSO algorithms mainly focusing on the DPSO. Afterward, a method for controlling the convergence rate of the DPSO using fractional calculus (FC) concepts is proposed. The fractional-order optimization algorithm, denoted as FO-DPSO, is tested using several well-known functions, and the relationship between the fractional-order velocity and the convergence of the algorithm is observed. Moreover, experimental results show that the FO-DPSO significantly outperforms the previously presented FO-PSO.


Fractional calculus DPSO Evolutionary algorithm 


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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • Micael S. Couceiro
    • 1
    • 2
    Email author
  • Rui P. Rocha
    • 2
  • N. M. Fonseca Ferreira
    • 1
  • J. A. Tenreiro Machado
    • 3
  1. 1.RoboCorp, Department of Electrotechnics EngineeringEngineering Institute of CoimbraCoimbraPortugal
  2. 2.Mobile Robotics Laboratory, Institute of Systems and RoboticsUniversity of CoimbraPólo 2Portugal
  3. 3.Department of Electrotechnics EngineeringEngineering Institute of PortoPortoPortugal

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